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Bessel functions are a family of solutions to Bessel's differential equation, which arises in various mathematical and physical problems involving circular symmetry. They are named after Friedrich Bessel, who studied these special functions extensively in the 19th century. Bessel functions have wide applications in physics, engineering, and mathematics, particularly in fields like heat conduction, wave propagation, diffraction analysis, and signal processing. These functions possess unique properties such as oscillatory behavior and exponential decay or growth depending on their order. They are also closely related to other mathematical functions like Hankel functions and modified Bessel functions. Bessel functions play a crucial role in understanding many natural phenomena and have been extensively studied by mathematicians and scientists over the years.

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